Simplify the following expression: $r = \dfrac{1}{7x} + \dfrac{1}{5x}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7x$ and $5x$ $\lcm(7x, 5x) = 35x$ $ r = \dfrac{5}{5} \cdot \dfrac{1}{7x} + \dfrac{7}{7} \cdot \dfrac{1}{5x} $ $r = \dfrac{5}{35x} + \dfrac{7}{35x}$ $r = \dfrac{5 +7}{35x}$ $r = \dfrac{12}{35x}$